In frequency division wireless communications, such as orthogonal frequency division multiplexing (OFDM), channel estimation is performed to estimate signal amplitude and phase shift caused by a given wireless channel. For pilot-based channel estimation, pilots and data tones may be distributed throughout a time-frequency resource block array, which is generally referred to as a physical resource unit (PRU) in the 802.16m standard and a resource block in the LTE standard. In order to perform channel estimation, calculations must be performed regularly, such as at the level of one PRU. Even at this level, a large number of calculations are involved to perform channel estimation. In the 802.16m standard, each communications sub-frame may transmit a preset number of symbols. In one example, the number of available frequency sub-carriers in a sub-frame may be 1728 and each PRU may contain 6 symbols times 18 sub-carriers such that one sub-frame corresponds to 96 PRUs.
Known channel estimation techniques using pilots distributed over a number of channels include linear minimum mean squared error (LMMSE) techniques. Due to calculational complexity, current channel estimation techniques typically apply simple one dimensional (1-D) LMMSE operations. However, in principle, two dimensional (2D) channel estimation, e.g., an LMMSE operation that treats at the same time all pilots and produces all channel estimates, is desirable due to its superior performance over single dimensional LMMSE, in which pilots are combined first along a frequency or time axis, and subsequently along the other axis. A drawback of using the 2D LMMSE is the matrix size: for a straightforward 2D LMMSE approach using a typical resource block size, the size of each matrix of coefficients relating the pilot values to the estimated channel on each subcarrier may range between 6×108 and 21×126, which corresponds to the number of pilots times the number of subcarriers in a PRU. Additionally, there are about 100 different matrices suitable for different transmission patterns when counting combinations of MIMO modes, interlacing versions, subframe durations, etc. Therefore, the total storage size for even a simple implementation of 2D LMMSE is about 120,000 coefficients per signal-to-noise ratio (SNR) point. In addition, in order to obtain improved channel estimation using 2D LMMSE by treating pilots of past sub-frames when possible, the number of pilots involved in the computation must be increased along with the complexity of calculation.
Furthermore, the optimal channel LMMSE estimation matrix is a function of the SNR and the channel model, which is typically composed of a power delay profile which describes the delay-spread, and Doppler spectrum which describes the time variability. Storing different matrices for each combination of SNR, channel conditions and pilot structure may be impractical, and therefore online calculation of these matrices is desirable. However, in a straight-forward implementation the calculation of the LMMSE channel estimation matrix requires complex matrix operations including matrix inversion of a matrix whose dimensions are the number of pilots, e.g., up to 21×21.
It is with respect to these and other considerations that the present improvements have been needed.